D0I:10.13374/1.issm100103.2008.05.020 第30卷第5期 北京科技大学学报 Vol.30 No.5 2008年5月 Journal of University of Science and Technology Beijing My2008 基于强度理论的岩石损伤弹塑性模型 王利)高 谦) 1)河南理工大学土木工程学院，焦作4540002)北京科技大学土木与环境工程学院，北京100083 摘要根据单轴受力特性曲线唯象地考察岩石材料损伤演化，定义弹性应变表示的一维损伤变量及其本构模型，利用双剪 强度理论将其推广至三维模型。塑性是潜在破坏面的摩擦滑移，在传统塑性理论的框架中，建立了基于摩尔一库仑强度理论与 潜在滑移面摩擦软硬化特性的各向异性损伤弹塑性本构关系。结果表明，计算的损伤演化与CT观测结果符合很好，用本文 的弹塑性模型反映损伤材料的力学特性是可行的. 关键词岩石；损伤模型；双剪理论：摩擦塑性 分类号TD853.36+4:0346.5 Elastoplastic model of damaged rock based on the strength theory WANG Li,GAO Qian2) 1)School of Civil Engineering.Henan Polytechnic University.Jiaozuo54000.China 2)Department of Civil and Environmental Engineering.University of Science and Technology Beijing.Beijing 100083.China ABSTRACI The one-dimensional damage variable was defined based on the elasto-brittle behavior of rock under uniaxial loading. To define the damage and its evolution in three-dimensional loading,the twin"shear theory was introduced to generalize the one-di- mensional damage model into the three-dimensional model.The elastic behavior of the damaged material under loading can be ex- pressed by reducing the elastic module,and the plastic flow can be represented by the slide on the plane between the two parts of the fractured rock.To establish the elastoplastic model of the damaged material.the concept of effective stress was used to contain the ef- fects of damage in the yielding equation as well as in the function of plastic potential.The model was established in the frame of the classical plasticity theory in which the Mohr-Coulomb criterion was employed as the yielding criterion,and the friction law on the pre- sliding plane was taken as the hardening"softening rule to describe the change of the yielding surface with the progressive yielding. The comparison of the calculated results with tested results by a CT machine shows that the damage model presented in the paper can accurately describe the damage evolution of rock in Nangiao Sandstone,and that the damage-elasto plastic model is indeed feasible in describing the mechanical properties of the damaged material. KEY WORDS rock:damage model:twin-shear theory:friction plasticity 岩石中存在着大量的随机分布的微裂纹，大量 岩石损伤的丰富信息，所以，建立在材料基本力学 细观实验观察表明)，岩石屈服破坏是一个微裂 特性基础上的唯象方法仍然是研究材料损伤及其演 纹萌生、扩展、贯通以及宏观裂隙面滑移的过程、在 化的重要方法，建立了很多损伤模型，如Loland、 连续介质力学中，用损伤和塑性来描述材料力学性 Marzars模型6]、周维垣的弹脆性损伤模型]、 质的这种不可逆变化， Lematre[s,Brook、高路彬等人的模型).唯象方法 对于损伤的描述，从材料的细观损伤机理出发， 的关键是如何实现从一维模型向三维模型的推广， 反映材料内部微裂纹、微孔洞等损伤基元演化行为 各模型基于损伤由拉应变产生、压应变不产生损伤 的模型已经有很多到，但是，最新揭示的损伤机 的细观机理，研究材料单元的单侧受力特性，在模型 理]表明，现有的细观损伤模型并不能够完全反映 中使用一个Heaviside算子来屏蔽压应变对损伤的 贡献，并以此建立三维各向异性损伤本构模型，研 收稿日期：2007-03-07修回日期：2007-10-22 究发现，上述模型适应能力差，某些情况下不能反映 作者简介：王利(1969一)，男，副教授，博士， 三轴应力下岩石损伤，本文提出了基于双剪强度理 E-mail:wlcjwh@163.com 论的三维各向同性损伤模型，计算结果与CT观测基于强度理论的岩石损伤弹塑性模型 王 利1） 高 谦2） 1） 河南理工大学土木工程学院‚焦作454000 2） 北京科技大学土木与环境工程学院‚北京100083 摘 要 根据单轴受力特性曲线唯象地考察岩石材料损伤演化‚定义弹性应变表示的一维损伤变量及其本构模型‚利用双剪 强度理论将其推广至三维模型．塑性是潜在破坏面的摩擦滑移‚在传统塑性理论的框架中‚建立了基于摩尔－库仑强度理论与 潜在滑移面摩擦软－硬化特性的各向异性损伤弹塑性本构关系．结果表明‚计算的损伤演化与 CT 观测结果符合很好‚用本文 的弹塑性模型反映损伤材料的力学特性是可行的． 关键词 岩石；损伤模型；双剪理论；摩擦塑性 分类号 TD853∙36＋4；O346∙5 Elastoplastic model of damaged rock based on the strength theory W A NG Li 1）‚GA O Qian 2） 1） School of Civil Engineering‚Henan Polytechnic University‚Jiaozuo454000‚China 2） Department of Civil and Environmental Engineering‚University of Science and Technology Beijing‚Beijing100083‚China ABSTRACT T he one-dimensional damage variable was defined based on the elasto-brittle behavior of rock under uniaxial loading． To define the damage and its evolution in three-dimensional loading‚the twin-shear theory was introduced to generalize the one-di￾mensional damage model into the three-dimensional model．T he elastic behavior of the damaged material under loading can be ex￾pressed by reducing the elastic module‚and the plastic flow can be represented by the slide on the plane between the two parts of the fractured rock．To establish the elastoplastic model of the damaged material‚the concept of effective stress was used to contain the ef￾fects of damage in the yielding equation as well as in the function of plastic potential．T he model was established in the frame of the classical plasticity theory in which the Mohr-Coulomb criterion was employed as the yielding criterion‚and the friction law on the pre￾sliding plane was taken as the hardening-softening rule to describe the change of the yielding surface with the progressive yielding． T he comparison of the calculated results with tested results by a CT machine shows that the damage model presented in the paper can accurately describe the damage evolution of rock in Nanqiao Sandstone‚and that the damage-elasto-plastic model is indeed feasible in describing the mechanical properties of the damaged material． KEY WORDS rock；damage model；twin-shear theory；friction plasticity 收稿日期：2007-03-07 修回日期：2007-10-22 作者简介：王 利（1969－）‚男‚副教授‚博士‚ E-mail：wlcjwh＠163．com 岩石中存在着大量的随机分布的微裂纹．大量 细观实验观察表明［1－3］‚岩石屈服破坏是一个微裂 纹萌生、扩展、贯通以及宏观裂隙面滑移的过程．在 连续介质力学中‚用损伤和塑性来描述材料力学性 质的这种不可逆变化． 对于损伤的描述‚从材料的细观损伤机理出发‚ 反映材料内部微裂纹、微孔洞等损伤基元演化行为 的模型已经有很多［4］．但是‚最新揭示的损伤机 理［5］表明‚现有的细观损伤模型并不能够完全反映 岩石损伤的丰富信息．所以‚建立在材料基本力学 特性基础上的唯象方法仍然是研究材料损伤及其演 化的重要方法‚建立了很多损伤模型‚如 Loland、 Marzars 模 型［6］、周 维 垣 的 弹 脆 性 损 伤 模 型［7］、 Lematre ［8］、Brook、高路彬等人的模型［9］．唯象方法 的关键是如何实现从一维模型向三维模型的推广‚ 各模型基于损伤由拉应变产生、压应变不产生损伤 的细观机理‚研究材料单元的单侧受力特性‚在模型 中使用一个 Heaviside 算子来屏蔽压应变对损伤的 贡献‚并以此建立三维各向异性损伤本构模型．研 究发现‚上述模型适应能力差‚某些情况下不能反映 三轴应力下岩石损伤．本文提出了基于双剪强度理 论的三维各向同性损伤模型‚计算结果与 CT 观测 第30卷 第5期 2008年 5月 北 京 科 技 大 学 学 报 Journal of University of Science and Technology Beijing Vol．30No．5 May2008 DOI:10．13374／j．issn1001－053x．2008．05．020